Andrew Svesko, University College London

Title: Microcanonical action of causal diamonds and the entropy of Hawking radiation

Abstract: The island formula, an extremization prescription for generalized entropy, is known to result in a Page curve for the entropy of Hawking radiation, arguably resolving the information paradox. The formula has been derived for Jackiw-Teitelboim gravity coupled to conformal matter in two-dimensional anti-de Sitter space using the replica trick. Thus far a derivation of the island formula for other gravitational theories remains elusive. In this talk, motivated by the thermodynamics of quantum extremal surfaces, I offer an alternative derivation. Specifically, I show how to derive the extremization of generalized entropy by minimizing the gravitational microcanonical action of an entanglement wedge, demonstrating consistency with the island formula. Crucially, this derivation holds for any  two-dimensional theory of semi-classical gravity.